Michael Huemer (2007) has articulated a provocative account of the concept of "epistemic possibility" which he hopes will explicate the explanatory value of the concept while also lending support to a broader anti-skeptical strategy. While I think his account has a number of advantages, many of which Huemer himself identifies, there are also significant disadvantages which should prompt us to seek an alternative. In this paper I describe an alternative which builds on some of the better features of Huemer's account, while avoiding its shortcomings. After having explained why this alternative avoids the problems I attribute to Huemer's position, I will conclude by presenting some independent considerations in favor of my account, which recommends that epistemic possibility claims be subjected to the same evidentialist standards to which belief and assertion are usually held accountable.